Natural Convection Inside an Inclined Wavy Enclosure Filled with a Porous Medium

Abstract

The Darcy flow model with the Boussinesq approximation is used to investigate numerically the natural convection inside an inclined wavy cavity filled with a porous medium. Finite Element Method is used to discretize the governing differential equations with non-staggered variable arrangement. Results are presented for $$0^{\circ}\leqslant \phi \leqslant 90^{\circ}, 10\leqslant Ra\leqslant 10^3, 1\leqslant A\leqslant 3$$ and $$0\leqslant \lambda \leqslant 0.3$$ , where ϕ, Ra, A and λ correspond to the cavity inclination angle, Rayleigh number, aspect ratio and surface waviness parameter, respectively. Stream and isotherm lines representing the corresponding flow and thermal fields, and local and average Nusselt numbers distribution expressing the rate of heat transfer are determined and shown on graphs and tables. A good agreement is observed between the present results and those known from the open literature. The flow and thermal structures found to be highly dependent on surface waviness for inclination angles less than 45°, especially for high Rayleigh numbers.